Principled Algorithms for Optimizing Generalized Metrics in Binary Classification

TL;DR

This paper introduces a new principled approach for optimizing complex binary classification metrics, providing algorithms with theoretical guarantees and demonstrating improved performance over existing methods.

Contribution

It proposes a novel framework that reformulates metric optimization as cost-sensitive learning, with new surrogate losses and algorithms supported by theoretical guarantees.

Findings

Algorithms with $H$-consistency guarantees

Finite-sample generalization bounds established

Experimental results show improved metric optimization performance

Abstract

In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary classification loss. However, optimizing these metrics present significant computational and statistical challenges. Existing approaches often rely on the characterization of the Bayes-optimal classifier, and use threshold-based methods that first estimate class probabilities and then seek an optimal threshold. This leads to algorithms that are not tailored to restricted hypothesis sets and lack finite-sample performance guarantees. In this work, we introduce principled algorithms for optimizing generalized metrics, supported by $H$-consistency and finite-sample generalization bounds. Our approach reformulates metric optimization as a generalized cost-sensitive learning problem, enabling the design of novel surrogate loss functions with provable $H$-consistency guarantees. Leveraging this framework, we develop new algorithms, METRO (Metric Optimization), with strong theoretical performance guarantees. We report the results of experiments demonstrating the effectiveness of our methods compared to prior baselines.